JEE Main 2022 — Optics

A convex lens has power $P$. It is cut into two halves along its principal axis. Further one piece (out of the two halves) is cut into two halves perpendicular to the principal axis (as shown in figures). Choose the incorrect option for the reported pieces. 

A convex lens of focal length $20\mathrm{cm}$ is placed in front of convex mirror with principal axis coinciding each other. The distance between the lens and mirror is $10\mathrm{cm}$. A point object is placed on principal axis at a distance of $60\mathrm{cm}$ from the convex lens. The image formed by combination coincides the object itself. The focal length of the convex mirror is _____ $\mathrm{cm}$.

A light ray is incident, at an incident angle ${\theta }_{1}$, on the system of two plane mirrors ${M}_{1}$ and ${M}_{2}$ having an inclination angle $75^{\circ}$ between them (as shown in figure). After reflecting from mirror ${M}_{1}$ it gets reflected back by the mirror ${M}_{2}$ with an angle of reflection $30^{\circ}$. The total deviation of the ray will be _____ degree. 

A light wave travelling linearly in a medium of dielectric constant $4$, incidents on the horizontal interface separating medium with air. The angle of incidence for which the total intensity of incident wave will be reflected back into the same medium will be : (Given : relative permeability of medium ${\mu }_{r}=1$)

A light whose electric field vectors are completely removed by using a good polaroid, allowed to incident on the surface of the prism at Brewster's angle. Choose the most suitable option for the phenomenon related to the prism.

A parallel beam of light is allowed to fall on a transparent spherical globe of diameter $30\mathrm{cm}$ and refractive index $1.5$. The distance from the centre of the globe at which beam of light can converge is _____ $\mathrm{mm}$.

A ray of light is incident at an angle of incidence $60^{\circ}$ on the glass slab of refractive index $\sqrt{3}$. After refraction, the light ray emerges out from other parallel faces and lateral shift between incident ray and emergent ray is $4\sqrt{3}\mathrm{cm}$. The thickness of the glass slab is _____ $\mathrm{cm}$.

A small bulb is placed at the bottom of a tank containing water to a depth of $\sqrt{7}m$. The refractive index of water is $\frac{4}{3}$. The area of the surface of water through which light from the bulb can emerge out is $x\pi {m}^{2}$. The value of $x$ is _____ .

A thin prism of angle $6^{\circ}$ and refractive index for yellow light $({n}_{Y})1.5$ is combined with another prism of angle $5^{\circ}$ and ${n}_{Y}=1.55$. The combination produces no dispersion. The net average deviation $(\delta )$ produced by the combination is ${(\frac{1}{x})}^{^{\circ}}$. The value of $x$ is _____ . 

A wave of frequency $=3\mathrm{GHz}$, strikes a particle of size ${(\frac{1}{100})}^{th}$ of $\lambda$, then this phenomenon is called as

An object '$O$' is placed at a distance of $100\mathrm{cm}$ in front of a concave mirror of radius of curvature $200\mathrm{cm}$ as shown in the figure. The object starts moving towards the mirror at a speed $2\mathrm{cm}{s}^{-1}$. The position of the image from the mirror after $10s$ will be at _____ $\mathrm{cm}$. 

An unpolarised light beam of intensity $2{I}_{0}$ is passed through a polaroid $P$ and then through another polaroid $Q$ which is oriented in such a way that its passing axis makes an angle of $30^{\circ}$ relative to that of $P$. The intensity of the emergent light is

As shown in the figure, after passing through the medium $1$. The speed of light ${v}_{2}$ in medium $2$ will be : (Given $c=3\times {10}^{8}m{s}^{-1}$) 

Consider a light ray travelling in air is incident into a medium of refractive index $\sqrt{2n}$. The incident angle is twice that of refracting angle. Then, the angle of incidence will be

For an object placed at a distance $2.4m$ from a lens, a sharp focused image is observed on a screen placed at a distance $12\mathrm{cm}$ from the lens. A glass plate of refractive index $1.5$ and thickness $1\mathrm{cm}$ is introduced between lens and screen such that the glass plate plane faces parallel to the screen. By what distance should the object be shifted so that a sharp focused image is observed again on the screen?

In a double slit experiment with monochromatic light, fringes are obtained on a screen placed at some distance from the plane of slits. If the screen is moved by $5\times {10}^{-2}m$ towards the slits, the change in fringe width is $3\times {10}^{-3}\mathrm{cm}$. If the distance between the slits is $1\mathrm{mm}$, then the wavelength of the light will be____$\mathrm{nm}$.

In a Young's double slit experiment, a laser light of $560\mathrm{nm}$ produces an interference pattern with consecutive bright fringes' separation of $7.2\mathrm{mm}$. Now another light is used to produce an interference pattern with consecutive bright fringes' separation of $8.1\mathrm{mm}$. The wavelength of second light is _____ $\mathrm{nm}.$

In a Young's double slit experiment, an angular width of the fringe is $0.35^{\circ}$ on a screen placed at $2m$ away for particular wavelength of $450\mathrm{nm}$. The angular width of the fringe, when whole system is immersed in a medium of refractive index $\frac{7}{5}$, is $\frac{1}{\alpha }$. The value of $\alpha$ is _____ .

In an experiment with a convex lens. The plot of the image distance $({v}^{'})$ against the object distance $({\mu }^{'})$ measured from the focus gives a curve ${v}^{'}{\mu }^{'}=225$. If all the distances are measured in $\mathrm{cm}$. The magnitude of the focal length of the lens is _____ $\mathrm{cm}$.

In normal adjustment, for a refracting telescope, the distance between objective and eye piece is $30\mathrm{cm}$. The focal length of the objective, when the angular magnification of the telescope is $2$, will be:

In the given figure, the face $AC$ of the equilateral prism is immersed in a liquid of refractive index $n$. For incident angle $60^{\circ}$ at the side $AC$, the refracted light beam just grazes along face $AC$. The refractive index of the liquid $n=\frac{\sqrt{x}}{4}$. The value of $x$ is _____ . (Given refractive index of glass $=1.5$) 

In young's double slit experiment performed using a monochromatic light of wavelength $\lambda$, when a glass plate $(\mu =1.5)$ of thickness $x\lambda$ is introduced in the path of the one of the interfering beams, the intensity at the position where the central maximum occurred previously remains unchanged. The value of $x$ will be

In young's double slit experiment, the fringe width is $12\mathrm{mm}$. If the entire arrangement is placed in water of refractive index $\frac{4}{3}$, then the fringe width becomes (in $\mathrm{mm}$)

In Young's double slit experiment the two slits are $0.6\mathrm{mm}$ distance apart. Interference pattern is observed on a screen at a distance $80\mathrm{cm}$ from the slits. The first dark fringe is observed on the screen directly opposite to one of the slits. The wavelength of light will be _____ $\mathrm{nm}$.

A thin prism of angle 6° and refractive index 1.5 is combined with another prism of angle 4° and refractive index 1.75...

In Youngs double slit experiment, fringe width is proportional to

Light enters from air into a given medium at an angle of $45^{\circ}$ with interface of the air-medium surface. After refraction, the light ray is deviated through an angle of $15^{\circ}$ from its original direction. The refractive index of the medium is :

Light travels in two media ${M}_{1}$ and ${M}_{2}$ with speeds $1.5\times {10}^{8}m{s}^{-1}$ and $2.0\times {10}^{8}m{s}^{-1}$ respectively. The critical angle between them is

Sodium light of wavelengths $650\mathrm{nm}$ and $655\mathrm{nm}$ is used to study diffraction at a single slit of aperture $0.5\mathrm{mm}$. The distance between the slit and the screen is $2.0m$. The separation between the positions of the first maxima of diffraction pattern obtained in the two cases is _____ $\times {10}^{-5}m$

The difference of speed of light in the two media $A$ and $B({v}_{A}-{v}_{B})$ is $2.6\times {10}^{7}m{s}^{-1}$. If the refractive index of medium $B$ is $1.47$, then the ratio of refractive index of medium $B$ to medium $A$ is: (Given : speed of light in vacuum $c=3\times {10}^{8}{ms}^{-1}$)

The graph between $\frac{1}{u}$ and $\frac{1}{v}$ for a thin convex lens in order to determine its focal length is plotted as shown in the figure. The refractive index of lens is $1.5$ and its both the surfaces have same radius of curvatures $R$. The value of $R$ will be _____ $\mathrm{cm}$. (Where $u=$ object distance, $v=$ image distance) 

The interference pattern is obtained with two coherent light sources of intensity ratio $4:1$. And the ratio $\frac{{I}_{\mathrm{max}}+{I}_{\mathrm{min}}}{{I}_{\mathrm{max}}-{I}_{\mathrm{min}}}$ is $\frac{5}{x}$. Then, the value of $x$ will be equal to :

The $X-Y$ plane be taken as the boundary between two transparent media ${M}_{1}$ and ${M}_{2}$. ${M}_{1}$ in $Z\geq 0$ has a refractive index of $\sqrt{2}$ and ${M}_{2}$ with $Z<0$ has a refractive index of $\sqrt{3}$. A ray of light travelling in ${M}_{1}$ along the direction given by the vector $\vec{A}=4\sqrt{3i}-3\sqrt{3}j-5\hat{k}$, is incident on the plane of separation. The value of difference between the angle of incident in ${M}_{1}$ and the angle of refraction in ${M}_{2}$ will be _____ degree.

The power of a lens (biconvex) is $1.25{m}^{-1}$ in particular medium. Refractive index of the lens is $1.5$ and radii of curvature are $20\mathrm{cm}$ and $40\mathrm{cm}$ respectively. The refractive index of surrounding medium:

The refracting angle of a prism is $A$ and refractive index of the material of the prism is $\mathrm{cot}(\frac{A}{2})$. Then the angle of minimum deviation will be

The speed of light in media $'A'$ and $'B'$ are $2.0\times {10}^{10}\mathrm{cm}{s}^{-1}$ and $1.5\times {10}^{10}\mathrm{cm}{s}^{-1}$ respectively. A ray of light enters from the medium $B$ to $A$ at an incident angle$'\theta '$. If the ray suffers total internal reflection, then

The two light beams having intensities $I$ and $9I$ interfere to produce a fringe pattern on a screen. The phase difference between the beams is $\frac{\pi }{2}$ at point $P$ and $\pi$ at point $Q$. Then the difference between the resultant intensities at $P$ and $Q$ will be :

Time taken by light to travel in two different materials $A$ and $B$ of refractive indices ${\mu }_{A}$ and ${\mu }_{B}$ of same thickness is ${t}_{1}$ and ${t}_{2}$ respectively. If ${t}_{2}-{t}_{1}=5\times {10}^{-10}s$ and the ratio of ${\mu }_{A}$ to ${\mu }_{B}$ is $1:2$. Then the thickness of material, in meter is: (Given ${v}_{A}$ and ${v}_{B}$ are velocities of light in $A$ and $B$ materials respectively).

Two beams of light having intensities $I$ and $4I$ interfere to produce a fringe pattern on a screen. The phase difference between the two beams are $\frac{\pi }{2}$ and $\frac{\pi }{3}$ at points $A$ and $B$ respectively. The difference between the resultant intensities at the two points is $xI$. The value of $x$ will be _____ .

Two coherent sources of light interfere. The intensity ratio of two sources is $1:4$. For this interference pattern if the value of $\frac{{I}_{\mathrm{max}}+{I}_{\mathrm{min}}}{{I}_{\mathrm{max}}-{I}_{\mathrm{min}}}$ is equal to $\frac{2\alpha +1}{\beta +3}$, then $\frac{\alpha }{\beta }$ will be

Two identical thin biconvex lenses of focal length $15\mathrm{cm}$ and refractive index $1.5$ are in contact with each other. The space between the lenses is filled with a liquid of refractive index $1.25$. The focal length of the combination is _____ $\mathrm{cm}.$

Using Young's double slit experiment, a monochromatic light of wavelength $5000Å$ produces fringes of fringe width $0.5\mathrm{mm}$. If another monochromatic light of wavelength $6000Å$ is used and the separation between the slits is doubled, then the new fringe width will be

Which of the following statement is correct?